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91.
Fukui Guo Yufeng Zhang Qingyou Yan 《International Journal of Theoretical Physics》2004,43(4):1139-1146
A new simple method for obtaining integrable hierarchies of soliton equations is proposed. First of all, a new loop algebra
is constructed, whose commutation operation is clear as that in loop algebra
. Second, by making use of the Tu scheme, many of integrable hierarchies with multicomponent potential functions can be produced. As a specific application of our method, a multicomponent AKNS hierarchy is obtained. Finally, an expanding loop algebra
of the loop algebra
is constructed. Taking advantage of
above, a type of integrable coupling system of the multicomponent AKNS hierarchy is worked out. 相似文献
92.
DU Beiliang WANG Jian Department of Mathematics Suzhou University Suzhou China Nantong Vocational College Nantong China 《中国科学A辑(英文版)》2004,47(3)
Let K_(m,n) be a complete bipartite graph with two partite sets having m and nvertices, respectively. A K_(p,q)-factorization of K_(m,n) is a set of edge-disjoint K_(p,q)-factorsof K_(m,n) which partition the set of edges of K_(m,n). When p=i and q is a prime number,Wang, in his paper "On K_(1,k)-factorizations of a complete bipartite graph" (Discrete Math,1994, 126; 359-364), investigated the K_(1,q)-factorization of K_(m,n) and gave a sufficientcondition for such a factorization to exist. In the paper "K_(1,k)-factorizations of completebipartite graphs" (Discrete Math, 2002, 259: 301-306), Du and Wang extended Wang'sresult to the case that q is any positive integer In this paper, we give a sufficient conditionfor K_(m,n) to have a K_(p,q)-factorization. As a special case, it is shown that the Martin's BACconjecture is true when p: q=k: (k+1) for any positive integer k. 相似文献
93.
We study a relaxation scheme of the Jin and Xin type for conservation laws with a flux function that depends discontinuously on the spatial location through a coefficient . If , we show that the relaxation scheme produces a sequence of approximate solutions that converge to a weak solution. The Murat-Tartar compensated compactness method is used to establish convergence. We present numerical experiments with the relaxation scheme, and comparisons are made with a front tracking scheme based on an exact Riemann solver. 相似文献
94.
95.
96.
We prove that the varieties
of complete pairs of zero-dimensional subschemes of lengths d
1 2, d
2 4 on a smooth irreducible projective algebraic surface are singular. 相似文献
97.
David Masson 《Designs, Codes and Cryptography》2003,28(3):283-302
We study (generalized) designs supported by words of given composition. We characterize them in terms of orthogonality relations with Specht modules; we define some zonal functions for the symmetric group and we give a closed formula for them, indexed on ordered pair of semi-standard generalized tableaux: Hahn polynomials are a particular case. We derive an algorithm to test if a set is a design. We use it to search designs in some ternary self-dual codes. 相似文献
98.
Paul Valery A. Bressler 《Compositio Mathematica》2003,135(3):245-278
We consider a fan as a ringed space (with finitely many points). We develop the corresponding sheaf theory and functors, such as direct image R* ( is a subdivision of a fan), Verdier duality, etc. The distinguished sheaf
, called the minimal sheaf plays the role of an equivariant intersection cohomology complex on the corresponding toric variety (which exists if is rational). Using
we define the intersection cohomology space IH(). It is conjectured that a strictly convex piecewise linear function on acts as a Lefschetz operator on IH(). We show that this conjecture implies Stanley's conjecture on the unimodality of the generalized h-vector of a convex polytope. 相似文献
99.
This paper concerns the cubic smoothing spline approach to nonparametric regression. After first deriving sharp asymptotic formulas for the eigenvalues of the smoothing matrix, the paper uses these formulas to investigate the efficiency of different selection criteria for choosing the smoothing parameter. Special attention is paid to the generalized maximum likelihood (GML), C
p
and extended exponential (EE) criteria and their marginal Bayesian interpretation. It is shown that (a) when the Bayesian model that motivates GML is true, using C
p
to estimate the smoothing parameter would result in a loss of efficiency with a factor of 10/3, proving and strengthening a conjecture proposed in Stein (1990); (b) when the data indeed come from the C
p
density, using GML would result in a loss of efficiency of ; (c) the loss of efficiency of the EE criterion is at most 1.543 when the data are sampled from its consistent density family. The paper not only studies equally spaced observations (the setting of Stein, 1990), but also investigates general sampling scheme of the design points, and shows that the efficiency results remain the same in both cases.This work is supported in part by NSF grant DMS-0204674 and Harvard University Clark-Cooke Fund.
Mathematics Subject Classification (2000):Primary: 62G08; Secondary: 62G20 相似文献
100.
Tong Yang Huijiang Zhao Changjiang Zhu 《Proceedings of the American Mathematical Society》2003,131(4):1257-1266
We give uniform BV estimates and -stability of Lax-Friedrichs' scheme for a class of systems of strictly hyperbolic conservation laws whose integral curves of the eigenvector fields are straight lines, i.e., Temple class, under the assumption of small total variation. This implies that the approximate solutions generated via the Lax-Friedrichs' scheme converge to the solution given by the method of vanishing viscosity or the Godunov scheme, and then the Glimm scheme or the wave front tracking method.